# June Prize Spotlight

Congratulations to Atul Dixit, the 2021 recipient of the Gábor Szegö Prize, and Sarah Peluse, the 2022 recipient of the Dénes König Prize. Learn more about the prize recipients below.

## Atul Dixit

Atul Dixit, Indian Institute of Technology Gandhinagar, is the 2021 recipient of the Gábor Szegö Prize. The award will be presented at the 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications, which will be held in a virtual format from June 13 – 17, 2022. Dixit will give a talk during the conference on Tuesday, June 14, at 9:00 a.m. EDT. The prize was awarded to Dixit for his impressive scientific work solving problems related to number theory using special functions, in particular related to the work of Ramanujan.

The SIAM Activity Group on Orthogonal Polynomials and Special Functions (SIAG/OPSF) awards the Gábor Szegö Prize every two years to one individual in their early career for outstanding research contributions in the area of orthogonal polynomials and special functions. The prize was originally scheduled to be awarded in 2021 at the 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications, which was later postponed to 2022.

Dixit is an Associate Professor of Mathematics at the Indian Institute of Technology Gandhinagar. He received his Bachelor’s degree in Computer Engineering from the University of Mumbai, India, in 2004; then a Master’s degree in Mathematics from Texas Tech University in 2006; followed by a Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign in 2012. He did his postdoctoral studies at Tulane University from 2012-2015 before joining IIT Gandhinagar as an Assistant Professor.

Dixit’s research interests are in analytic number theory, special functions, theory of partitions, q-series, and modular forms. He also likes to work in the areas of mathematics developed by Srinivasa Ramanujan.

**Q: Why are you excited to receive the Gábor Szegö Prize?**

**A**: It is heartening to see that the work I have done in special functions and analytic number theory over the past decade or so is getting recognition. There are important and exciting problems at the interface of these two areas which I have tried to focus my attention on, and yet the stock of such problems is hardly depleted. This award will definitely give a boost to my career and will motivate me to perform better than before. Any award comes with a responsibility of delivering better than before and this award will constantly remind me of it.

**Q: Could you tell us a bit about the research that won you the prize?**

**A**: The selection committee says this prize was awarded to me for “solving problems related to number theory using special functions, in particular related to the work of Ramanujan.”

Indeed, my mathematical research is at the interface of analytic number theory and special functions. Sometimes, my work in analytic number theory has led me to discover new interesting special functions such as generalized modified Bessel and Hurwitz zeta functions. Likewise, my work on special functions has frequently had implications in number theory, such as the one on generalized Lambert series or on the Voronoï summation formulas. I am hopeful that some of the work that I have done in special functions, especially the theories of generalized modified Bessel and Hurwitz zeta functions, will find its applications in mathematics as well as in engineering and sciences. I think my 2017 paper from *Advances in Mathematics* – titled “New pathways and connections in number theory and analysis motivated by two incorrect claims of Ramanujan,” joint with Bruce C. Berndt, Arindam Roy, and Alexandru Zaharescu – was one of the key papers that may have played an important role towards my selection for the award.

**Q: What does your work mean to the public?**

**A**: Special functions is a branch of mathematics catering to the needs of not only both pure and applied mathematicians but also scientists working in pure or applied areas. I am hopeful that some of the work that I have done in special functions and number theory, especially by initiating the theories of generalized modified Bessel and Hurwitz zeta functions will eventually find its applications in mathematics as well as in engineering and sciences, as these functions are natural generalizations of Bessel and Hurwitz zeta functions arising in my work on generalized modular relations and are not artificially concocted. Similarly, I hope my work on generalized Lambert series will have implications in transcendental number theory.

**Q: What does being a member of SIAM mean to you?**

**A**: Being a member of SIAM means a lot to me. The first time I heard about SIAM was in 2005 when I was a first year M.S. student in Mathematics at Texas Tech University. Since then, I have always followed the excellent resources that SIAM provides for us – be it excellent, top-notch journals like *SIAM Journal on Mathematical Analysis* that frequently has articles useful for my research, or the OPSFA conferences that SIAM hosts every two years. For example, I attended the 2015 OPSFA-13 conference in Gaithersburg, Maryland. It was a fabulous conference, and I enjoyed the participation from a huge number of excellent mathematicians. Intellectually, it was quite enriching for me. Another aspect of SIAM I really like is its all-inclusiveness in having participation of members from all parts of the world in its committees, student chapters, etc.

## Sarah Peluse

Sarah Peluse is the 2022 recipient of the Dénes König Prize, which will be awarded at the 2022 SIAM Conference on Discrete Mathematics (DM22) to be held in person only from June 14 – 16, 2022 in Pittsburgh, Pennsylvania, U.S. Peluse will give a talk at the conference titled, “Quantitative Bounds in the Polynomial Szemerédi Theorem and Related Results,” on Tuesday, June 14 at 1:30 p.m. EDT.

The prize was awarded to Peluse for her paper, "Bounds For Sets With No Polynomial Progressions," matching the Gowers bounds for arithmetic progressions for the more general class of polynomial patterns.

The SIAM Activity Group on Discrete Mathematics awards the Dénes König Prize every two years to an individual or individuals in their early career for outstanding research contributions in an area of discrete mathematics, as evidenced by a publication in a peer-reviewed journal within the three calendar years prior to the award year.

Sarah Peluse is a Veblen research instructor at Princeton University and the Institute for Advanced Study. She earned an A.B. from the University of Chicago and Ph.D. from Stanford University, both in mathematics. Her research interests are in additive combinatorics and analytic number theory.

**Q: Why are you excited to receive the Dénes König Prize?**

**A**: I'm very honored to receive the Dénes König Prize! I am happy to see that my work in additive combinatorics apparently has broader appeal in discrete math.

**Q: Could you tell us a bit about the research that won you the prize?**

**A**: The polynomial Szemer\'edi theorem, which is due to Bergelson and Leibman, says that any subset of the integers with positive upper density contains any reasonable polynomial progression. Quantitative bounds in this theorem were, for a long time, only known for a couple of very special polynomial progressions. I proved the first quantitative bounds for a large family of new polynomial progressions. This wouldn't have been possible without prior joint work with Sean Prendiville, which contained several crucial insights.

**Q: What does your work mean to the public?**

**A**: Aside from contributing a bit to humanity's collective mathematical knowledge, not much!

**Q: What does being a member of SIAM mean to you?**

**A**: I am grateful for SIAM's excellent conferences and journals, from which I have learned a lot.